McGeady, who is out of contract next summer, was placed on the transfer list by Spartak last week after a reported fall-out with coach Valery Karpin.

The 27-year-old indicated in November that he would not sign another deal to stay in Moscow, and is free to negotiate with other clubs from Jan. 1.

According to sources, Martinez is keen to bring McGeady to Goodison Park, with the likeliest route being a precontract agreement ahead of a free transfer next summer.

The Everton boss, though, has refused to speak publicly about the possibility of a deal for the winger, and was coy again when asked on Friday.

Instead, he talked of the need to strengthen in January to bolster a squad which has lost striker Arouna Kone and midfielder Darron Gibson to long-term knee injuries.

Martinez said: “As you know, we’re going to use the window in January to try to help the team, because we lost two players, in Arouna Kone and Darron Gibson, who I feel are very important for us in the long-term.

“We’ll see if we can identify one or two players who can help the group. In terms of who those players are going to be, unless they’re out of contract, we’ll never mention players if they are registered with other clubs.

“We’ve been working really hard so far to identify who can help the group, but it’s not going to be a case of just signing anyone. It has to be a specific personality who can bring certain qualities to the side. That’s what we’re looking for in January.”

Martinez indicated that neither Kone nor Gibson, both recovering from surgery after suffering their injuries in October, are likely to play again this season.

The Spaniard will also continue to be without left-back Leighton Baines for Sunday’s Premier League trip to Arsenal.

Baines has missed Everton’s last two matches with a fractured toe, and is set to be out until the New Year.

Martinez said: “Leighton Baines is recovering really, really well. But three or four weeks is probably the margin we are giving ourselves before we see Leighton back.”

Bryan Oviedo, Baines’ deputy, made the most of a rare start by scoring the winner as Everton earned a 1-0 victory at Manchester United on Wednesday.

But despite witnessing an impressive performance from the Costa Rican, Martinez insists he has no intention of losing Baines, the subject of interest from United.

He said: “Nothing changes. We’re in the middle of the season, we’ve played 14 games. The only thing we’re thinking about is finishing the season with the strongest squad possible.

“The last thing we want is to lose experienced players. These players mean a lot to Everton and represent a lot in terms of what we want to achieve. It doesn’t change anything.”

Wednesday’s win was Everton’s first at Old Trafford since 1992, and Martinez wants his side to end another of their away jinxes on Sunday.

The Merseysiders have not enjoyed an away win over Arsenal since Graham Stuart and Andrei Kanchelskis scored in a 2-1 Premier League victory at Highbury in January 1996.

Martinez acknowledges that it will be tough to overcome Arsene Wenger’s side, who are four points clear at the top of the Premier League, but he wants Everton to show the kind of self-belief that brought them a win at Old Trafford.

He said: “Arsenal deserve a lot of respect. If you’re capable of winning 11 of your first 14 games, you are the outstanding team in the competition. That’s why we’ll have to be at our best.

“But again, we’ll be looking at this as a terrific test to see how quickly we can improve and challenge these sort of sides.”

Meanwhile, Martinez has added his voice to the numerous tributes from the sporting world paid to former South African president and anti-apartheid icon Nelson Mandela, who has died at the age of 95.

He said: “He was an incredible leader, not just from a political point of view but as a human. The human side was incredible. He was an inspiration. I’m sure everyone around the world will have some memory of Nelson Mandela. He was a terrific man.”